Theresa May has told EU leaders she is ready to keep the UK under single market and customs union rules for an extra year after Brexit in the absence of any solutions to the impasse over the Irish border.

At the start of a summit that had previously been earmarked as the deadline for a breakthrough, both sides admitted the deadlock would take more time to untangle and said they were willing to extend the post-Brexit transition until the end of 2021.

British Prime Minister Theresa May, left, hugs Jean-Claude Juncker, President of the European Commission, as they meet in Brussels, Wednesday, Oct. 17, 2018 when European leaders meet to negotiate on terms of Britain's divorce from the European Union. (AP Photo/Francisco Seco)

The admission will anger Brexiteers in the Conservative Party and pose a particular challenge to Scottish Conservative MPs, who have argued strongly for a swift exit from the Common Fisheries Policy.

She added: “The last stage will need courage, trust and leadership on both sides.”

A UK source said the Prime Minister issued an appeal “to find a creative way out of this dilemma” on the Irish border and reiterated she was “fully committed to finding a legally operative backstop” that guarantees no hard border in Ireland.

However, despite a call from European Council president Donald Tusk for “new facts” on the Irish border, there was little evidence of fresh proposals to break the stalemate.

Speaking after hearing Mrs May’s address to EU leaders, European Parliament president Antonio Tajani said: “There was a message of goodwill and readiness to reach an agreement, but I didn’t perceive anything substantially new in terms of content as I listened to Mrs May.”

Mr Tajani added the Prime Minister had said she was willing to consider a proposal from the EU to extend the transition period.

An EU source confirmed Mrs May was ready to consider adding an extra year.

Arriving at the summit, EU chief Brexit negotiator Michel Barnier had told reporters that “much more time” was needed to reach a breakthrough.

“We are not there yet ... we will continue the work in the next weeks calmly and patiently,” he said.

EU leaders must now decide whether to hold an emergency summit next month, despite warnings from leaders including French president Emmanuel Macron that no further meeting could take place without progress on the Irish border.

A November summit could be used to focus on preparations for a no-deal Brexit.

A final Brexit deal could now be put off until as late as December – beyond the point at which Mr Barnier had said an agreement was essential.

The French Government yesterday published draft no-deal legislation that could require British citizens to obtain a visa before travelling to France following the UK’s withdrawal from the EU.

EU leaders voiced frustration at Mrs May’s inability to command the full support of her party.

Lithuanian president Dalia Grybauskaite claimed the Prime Minister didn’t have a “strong mandate”.

Ms Grybauskaite said it was difficult for the EU to “negotiate with a person who has no full support of the position”.

And Belgian Prime Minister Charles Michel said last night: “We are concerned because we see it is difficult in the British Parliament to have the same views on the future of the relationship between the EU and UK.”